© 2015. The American Astronomical Society. All rights reserved. The hot Jupiter WASP-43b (2 MJ, 1 RJ, Torb= 19.5 hr) has now joined the ranks of transiting hot Jupiters HD 189733b and HD 209458b as an exoplanet with a large array of observational constraints. Because WASP-43b receives a similar stellar flux as HD 209458b but has a rotation rate four times faster and a higher gravity, studying WASP-43b probes the effect of rotation rate and gravity on the circulation when stellar irradiation is held approximately constant. Here we present three-dimensional (3D) atmospheric circulation models of WASP-43b, exploring the effects of composition, metallicity, and frictional drag. We find that the circulation regime of WASP-43b is not unlike other hot Jupiters, with equatorial superrotation that yields an eastward-shifted hotspot and large day-night temperature variations (600 K at photospheric pressures). We then compare our model results to Hubble Space Telescope (HST)/WFC3 spectrophotometric phase curve measurements of WASP-43b from 1.12 to 1.65 μm. Our results show the 5× solar model light curve provides a good match to the data, with a peak flux phase offset and planet/star flux ratio that is similar to observations; however, the model nightside appears to be brighter. Nevertheless, our 5× solar model provides an excellent match to the WFC3 dayside emission spectrum. This is a major success, as the result is a natural outcome of the 3D dynamics with no model tuning. These results demonstrate that 3D circulation models can help interpret exoplanet atmospheric observations, even at high resolution, and highlight the potential for future observations with HST, James Webb Space Telescope, and other next-generation telescopes.